The MIMO technique has been introduced into mRCs to allow spatial multiplexing. In a MIMO mRC, as each user in general transmits multiple spatial streams, a new challenge to be addressed is to mitigate the inter-stream interference at the relay and at the user ends.
Degrees of freedom (DoF) is a critical metric in characterizing the fundamental capacity of a wireless network [1]}, [2]}. The DoF of the MIMO mRC
has been previously studied in [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. For example,
the authors in [4]} investigated the DoF capacity of the MIMO Y channel (a special case of the MIMO mRC with three users)
and showed that the DoF capacity can be achieved when \(\frac{M}{N}\ge \frac{2}{3}\) , where \(M\)  denotes the number of antennas at each user, and \(N\)  denotes the number of antennas at the relay.
The authors in [6]} generalized the results in [4]} by considering a three-user asymmetric MIMO Y channel with different numbers of antennas at the users, and proved that the DoF capacity can be achieved for arbitrary antenna setups. Recently, as parallel to the work in this paper, the work in [7]} established the DoF capacity of the four-user symmetric MIMO Y channel for arbitrary antenna setups.
Further, the authors
in [8]}, [9]}
studied more general data exchange models in which the users in the network are grouped into clusters, and each user in a cluster exchanges information only with the other users in the same cluster. In particular, the authors in [8]} derived sufficient conditions on the antenna configuration to achieve the DoF capacity of a clustered mRC with pairwise data exchange, in which each user in a cluster sends a different message to each of the other users in the same cluster. Note that the data exchange models considered in [4]} and [5]} can be regarded as
the one-cluster case of the model studied in [8]}.
Moreover, the author in [9]} derived an achievable DoF for a clustered MIMO mRC with full data exchange, i.e., each user in a cluster delivers a common message to all the other users in the same cluster.
